How do you solve #x^2 - 8x = 20#?

Question

Genesis Allen · Accepted Answer

x= -10, 2

First, take the 20 to the other side so the equation is equal to 0. Now the equation should look like this: #x^2-8x-20=0#. Now factor the equation using the big X. What multiplies to -20 and adds to -8? The factors should be (x-10) and (x+2). To find what x is equal to make the factors equal to 0. (x-10)=0 is 10 and (x+2)=0 is -2.

Julia Adams · Answer

undefined To solve the equation $x^2 - 8x = 20$, follow these steps:

1. Move all terms to one side to set the equation equal to zero:
   $x^2 - 8x - 20 = 0$.

2. Use the quadratic formula to find the solutions for $x$:
   $x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}$,
   where $a = 1$, $b = -8$, and $c = -20$.

3. Substitute the values of $a$, $b$, and $c$ into the quadratic formula and solve for $x$:

$x = \frac{{-(-8) \pm \sqrt{{(-8)^2 - 4 \cdot 1 \cdot (-20)}}}}{{2 \cdot 1}}$

$x = \frac{{8 \pm \sqrt{{64 + 80}}}}{2}$

$x = \frac{{8 \pm \sqrt{{144}}}}{2}$

$x = \frac{{8 \pm 12}}{2}$

4. Solve for both values of $x$ by performing addition and subtraction:

$x_1 = \frac{{8 + 12}}{2} = \frac{20}{2} = 10$

$x_2 = \frac{{8 - 12}}{2} = \frac{-4}{2} = -2$

Therefore, the solutions for the equation $x^2 - 8x = 20$ are $x = 10$ and $x = -2$.